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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.random;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.linear.RealMatrix;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.linear.RectangularCholeskyDecomposition;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    /**<a name="line.24"></a>
<FONT color="green">025</FONT>     * A {@link RandomVectorGenerator} that generates vectors with with<a name="line.25"></a>
<FONT color="green">026</FONT>     * correlated components.<a name="line.26"></a>
<FONT color="green">027</FONT>     * &lt;p&gt;Random vectors with correlated components are built by combining<a name="line.27"></a>
<FONT color="green">028</FONT>     * the uncorrelated components of another random vector in such a way that<a name="line.28"></a>
<FONT color="green">029</FONT>     * the resulting correlations are the ones specified by a positive<a name="line.29"></a>
<FONT color="green">030</FONT>     * definite covariance matrix.&lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;The main use for correlated random vector generation is for Monte-Carlo<a name="line.31"></a>
<FONT color="green">032</FONT>     * simulation of physical problems with several variables, for example to<a name="line.32"></a>
<FONT color="green">033</FONT>     * generate error vectors to be added to a nominal vector. A particularly<a name="line.33"></a>
<FONT color="green">034</FONT>     * interesting case is when the generated vector should be drawn from a &lt;a<a name="line.34"></a>
<FONT color="green">035</FONT>     * href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution"&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     * Multivariate Normal Distribution&lt;/a&gt;. The approach using a Cholesky<a name="line.36"></a>
<FONT color="green">037</FONT>     * decomposition is quite usual in this case. However, it can be extended<a name="line.37"></a>
<FONT color="green">038</FONT>     * to other cases as long as the underlying random generator provides<a name="line.38"></a>
<FONT color="green">039</FONT>     * {@link NormalizedRandomGenerator normalized values} like {@link<a name="line.39"></a>
<FONT color="green">040</FONT>     * GaussianRandomGenerator} or {@link UniformRandomGenerator}.&lt;/p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;p&gt;Sometimes, the covariance matrix for a given simulation is not<a name="line.41"></a>
<FONT color="green">042</FONT>     * strictly positive definite. This means that the correlations are<a name="line.42"></a>
<FONT color="green">043</FONT>     * not all independent from each other. In this case, however, the non<a name="line.43"></a>
<FONT color="green">044</FONT>     * strictly positive elements found during the Cholesky decomposition<a name="line.44"></a>
<FONT color="green">045</FONT>     * of the covariance matrix should not be negative either, they<a name="line.45"></a>
<FONT color="green">046</FONT>     * should be null. Another non-conventional extension handling this case<a name="line.46"></a>
<FONT color="green">047</FONT>     * is used here. Rather than computing &lt;code&gt;C = U&lt;sup&gt;T&lt;/sup&gt;.U&lt;/code&gt;<a name="line.47"></a>
<FONT color="green">048</FONT>     * where &lt;code&gt;C&lt;/code&gt; is the covariance matrix and &lt;code&gt;U&lt;/code&gt;<a name="line.48"></a>
<FONT color="green">049</FONT>     * is an upper-triangular matrix, we compute &lt;code&gt;C = B.B&lt;sup&gt;T&lt;/sup&gt;&lt;/code&gt;<a name="line.49"></a>
<FONT color="green">050</FONT>     * where &lt;code&gt;B&lt;/code&gt; is a rectangular matrix having<a name="line.50"></a>
<FONT color="green">051</FONT>     * more rows than columns. The number of columns of &lt;code&gt;B&lt;/code&gt; is<a name="line.51"></a>
<FONT color="green">052</FONT>     * the rank of the covariance matrix, and it is the dimension of the<a name="line.52"></a>
<FONT color="green">053</FONT>     * uncorrelated random vector that is needed to compute the component<a name="line.53"></a>
<FONT color="green">054</FONT>     * of the correlated vector. This class handles this situation<a name="line.54"></a>
<FONT color="green">055</FONT>     * automatically.&lt;/p&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>     *<a name="line.56"></a>
<FONT color="green">057</FONT>     * @version $Id: CorrelatedRandomVectorGenerator.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.57"></a>
<FONT color="green">058</FONT>     * @since 1.2<a name="line.58"></a>
<FONT color="green">059</FONT>     */<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>    public class CorrelatedRandomVectorGenerator<a name="line.61"></a>
<FONT color="green">062</FONT>        implements RandomVectorGenerator {<a name="line.62"></a>
<FONT color="green">063</FONT>        /** Mean vector. */<a name="line.63"></a>
<FONT color="green">064</FONT>        private final double[] mean;<a name="line.64"></a>
<FONT color="green">065</FONT>        /** Underlying generator. */<a name="line.65"></a>
<FONT color="green">066</FONT>        private final NormalizedRandomGenerator generator;<a name="line.66"></a>
<FONT color="green">067</FONT>        /** Storage for the normalized vector. */<a name="line.67"></a>
<FONT color="green">068</FONT>        private final double[] normalized;<a name="line.68"></a>
<FONT color="green">069</FONT>        /** Root of the covariance matrix. */<a name="line.69"></a>
<FONT color="green">070</FONT>        private final RealMatrix root;<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>        /**<a name="line.72"></a>
<FONT color="green">073</FONT>         * Builds a correlated random vector generator from its mean<a name="line.73"></a>
<FONT color="green">074</FONT>         * vector and covariance matrix.<a name="line.74"></a>
<FONT color="green">075</FONT>         *<a name="line.75"></a>
<FONT color="green">076</FONT>         * @param mean Expected mean values for all components.<a name="line.76"></a>
<FONT color="green">077</FONT>         * @param covariance Covariance matrix.<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param small Diagonal elements threshold under which  column are<a name="line.78"></a>
<FONT color="green">079</FONT>         * considered to be dependent on previous ones and are discarded<a name="line.79"></a>
<FONT color="green">080</FONT>         * @param generator underlying generator for uncorrelated normalized<a name="line.80"></a>
<FONT color="green">081</FONT>         * components.<a name="line.81"></a>
<FONT color="green">082</FONT>         * @throws org.apache.commons.math3.linear.NonPositiveDefiniteMatrixException<a name="line.82"></a>
<FONT color="green">083</FONT>         * if the covariance matrix is not strictly positive definite.<a name="line.83"></a>
<FONT color="green">084</FONT>         * @throws DimensionMismatchException if the mean and covariance<a name="line.84"></a>
<FONT color="green">085</FONT>         * arrays dimensions do not match.<a name="line.85"></a>
<FONT color="green">086</FONT>         */<a name="line.86"></a>
<FONT color="green">087</FONT>        public CorrelatedRandomVectorGenerator(double[] mean,<a name="line.87"></a>
<FONT color="green">088</FONT>                                               RealMatrix covariance, double small,<a name="line.88"></a>
<FONT color="green">089</FONT>                                               NormalizedRandomGenerator generator) {<a name="line.89"></a>
<FONT color="green">090</FONT>            int order = covariance.getRowDimension();<a name="line.90"></a>
<FONT color="green">091</FONT>            if (mean.length != order) {<a name="line.91"></a>
<FONT color="green">092</FONT>                throw new DimensionMismatchException(mean.length, order);<a name="line.92"></a>
<FONT color="green">093</FONT>            }<a name="line.93"></a>
<FONT color="green">094</FONT>            this.mean = mean.clone();<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>            final RectangularCholeskyDecomposition decomposition =<a name="line.96"></a>
<FONT color="green">097</FONT>                new RectangularCholeskyDecomposition(covariance, small);<a name="line.97"></a>
<FONT color="green">098</FONT>            root = decomposition.getRootMatrix();<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>            this.generator = generator;<a name="line.100"></a>
<FONT color="green">101</FONT>            normalized = new double[decomposition.getRank()];<a name="line.101"></a>
<FONT color="green">102</FONT>    <a name="line.102"></a>
<FONT color="green">103</FONT>        }<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>        /**<a name="line.105"></a>
<FONT color="green">106</FONT>         * Builds a null mean random correlated vector generator from its<a name="line.106"></a>
<FONT color="green">107</FONT>         * covariance matrix.<a name="line.107"></a>
<FONT color="green">108</FONT>         *<a name="line.108"></a>
<FONT color="green">109</FONT>         * @param covariance Covariance matrix.<a name="line.109"></a>
<FONT color="green">110</FONT>         * @param small Diagonal elements threshold under which  column are<a name="line.110"></a>
<FONT color="green">111</FONT>         * considered to be dependent on previous ones and are discarded.<a name="line.111"></a>
<FONT color="green">112</FONT>         * @param generator Underlying generator for uncorrelated normalized<a name="line.112"></a>
<FONT color="green">113</FONT>         * components.<a name="line.113"></a>
<FONT color="green">114</FONT>         * @throws org.apache.commons.math3.linear.NonPositiveDefiniteMatrixException<a name="line.114"></a>
<FONT color="green">115</FONT>         * if the covariance matrix is not strictly positive definite.<a name="line.115"></a>
<FONT color="green">116</FONT>         */<a name="line.116"></a>
<FONT color="green">117</FONT>        public CorrelatedRandomVectorGenerator(RealMatrix covariance, double small,<a name="line.117"></a>
<FONT color="green">118</FONT>                                               NormalizedRandomGenerator generator) {<a name="line.118"></a>
<FONT color="green">119</FONT>            int order = covariance.getRowDimension();<a name="line.119"></a>
<FONT color="green">120</FONT>            mean = new double[order];<a name="line.120"></a>
<FONT color="green">121</FONT>            for (int i = 0; i &lt; order; ++i) {<a name="line.121"></a>
<FONT color="green">122</FONT>                mean[i] = 0;<a name="line.122"></a>
<FONT color="green">123</FONT>            }<a name="line.123"></a>
<FONT color="green">124</FONT>    <a name="line.124"></a>
<FONT color="green">125</FONT>            final RectangularCholeskyDecomposition decomposition =<a name="line.125"></a>
<FONT color="green">126</FONT>                new RectangularCholeskyDecomposition(covariance, small);<a name="line.126"></a>
<FONT color="green">127</FONT>            root = decomposition.getRootMatrix();<a name="line.127"></a>
<FONT color="green">128</FONT>    <a name="line.128"></a>
<FONT color="green">129</FONT>            this.generator = generator;<a name="line.129"></a>
<FONT color="green">130</FONT>            normalized = new double[decomposition.getRank()];<a name="line.130"></a>
<FONT color="green">131</FONT>    <a name="line.131"></a>
<FONT color="green">132</FONT>        }<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>        /** Get the underlying normalized components generator.<a name="line.134"></a>
<FONT color="green">135</FONT>         * @return underlying uncorrelated components generator<a name="line.135"></a>
<FONT color="green">136</FONT>         */<a name="line.136"></a>
<FONT color="green">137</FONT>        public NormalizedRandomGenerator getGenerator() {<a name="line.137"></a>
<FONT color="green">138</FONT>            return generator;<a name="line.138"></a>
<FONT color="green">139</FONT>        }<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>        /** Get the rank of the covariance matrix.<a name="line.141"></a>
<FONT color="green">142</FONT>         * The rank is the number of independent rows in the covariance<a name="line.142"></a>
<FONT color="green">143</FONT>         * matrix, it is also the number of columns of the root matrix.<a name="line.143"></a>
<FONT color="green">144</FONT>         * @return rank of the square matrix.<a name="line.144"></a>
<FONT color="green">145</FONT>         * @see #getRootMatrix()<a name="line.145"></a>
<FONT color="green">146</FONT>         */<a name="line.146"></a>
<FONT color="green">147</FONT>        public int getRank() {<a name="line.147"></a>
<FONT color="green">148</FONT>            return normalized.length;<a name="line.148"></a>
<FONT color="green">149</FONT>        }<a name="line.149"></a>
<FONT color="green">150</FONT>    <a name="line.150"></a>
<FONT color="green">151</FONT>        /** Get the root of the covariance matrix.<a name="line.151"></a>
<FONT color="green">152</FONT>         * The root is the rectangular matrix &lt;code&gt;B&lt;/code&gt; such that<a name="line.152"></a>
<FONT color="green">153</FONT>         * the covariance matrix is equal to &lt;code&gt;B.B&lt;sup&gt;T&lt;/sup&gt;&lt;/code&gt;<a name="line.153"></a>
<FONT color="green">154</FONT>         * @return root of the square matrix<a name="line.154"></a>
<FONT color="green">155</FONT>         * @see #getRank()<a name="line.155"></a>
<FONT color="green">156</FONT>         */<a name="line.156"></a>
<FONT color="green">157</FONT>        public RealMatrix getRootMatrix() {<a name="line.157"></a>
<FONT color="green">158</FONT>            return root;<a name="line.158"></a>
<FONT color="green">159</FONT>        }<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>        /** Generate a correlated random vector.<a name="line.161"></a>
<FONT color="green">162</FONT>         * @return a random vector as an array of double. The returned array<a name="line.162"></a>
<FONT color="green">163</FONT>         * is created at each call, the caller can do what it wants with it.<a name="line.163"></a>
<FONT color="green">164</FONT>         */<a name="line.164"></a>
<FONT color="green">165</FONT>        public double[] nextVector() {<a name="line.165"></a>
<FONT color="green">166</FONT>    <a name="line.166"></a>
<FONT color="green">167</FONT>            // generate uncorrelated vector<a name="line.167"></a>
<FONT color="green">168</FONT>            for (int i = 0; i &lt; normalized.length; ++i) {<a name="line.168"></a>
<FONT color="green">169</FONT>                normalized[i] = generator.nextNormalizedDouble();<a name="line.169"></a>
<FONT color="green">170</FONT>            }<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>            // compute correlated vector<a name="line.172"></a>
<FONT color="green">173</FONT>            double[] correlated = new double[mean.length];<a name="line.173"></a>
<FONT color="green">174</FONT>            for (int i = 0; i &lt; correlated.length; ++i) {<a name="line.174"></a>
<FONT color="green">175</FONT>                correlated[i] = mean[i];<a name="line.175"></a>
<FONT color="green">176</FONT>                for (int j = 0; j &lt; root.getColumnDimension(); ++j) {<a name="line.176"></a>
<FONT color="green">177</FONT>                    correlated[i] += root.getEntry(i, j) * normalized[j];<a name="line.177"></a>
<FONT color="green">178</FONT>                }<a name="line.178"></a>
<FONT color="green">179</FONT>            }<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>            return correlated;<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>        }<a name="line.183"></a>
<FONT color="green">184</FONT>    <a name="line.184"></a>
<FONT color="green">185</FONT>    }<a name="line.185"></a>




























































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